what-is-the-volume-in-cubic-inches-of-a-cube-whose-total-surface-area-is-216-square-inches-beginequa

Question

What is the volume, in cubic inches, of a cube whose total surface
area is 216 square inches?
\begin{equation}
\begin{array}{l}{	ext { (A) } 18} \ {	ext { (B) } 36}\{	ext { (C) } 216} \ {	ext { (D) } 1,296}\end{array}
\end{equation}

Lily An · Accepted Answer

can, this one says. What is the volume in cubic inches of acute, whose total surface area is two hundred and sixteen square inches? First of all, let&#x27;s think about the equation for the surface area of a cute for a service area. If it&#x27;s a queue, you know that all the six sides are equal, so we could just take one of the sides areas and multiply that by six. So area on one side time. Six. So then what&#x27;s the area of one side? We know that because it&#x27;s a cube, it&#x27;s actually just made up of six squares, which means it&#x27;s just gonna be length times length, because the length and the width should be the same. So we could just call that length times width length when we know it&#x27;s gonna be six l squared, and we know that the six all squared in this particular Kew is going to be two sixteen square inches. Co. Tells us that the total surface area there&#x27;s two sixteen, so then we just have to first of all, isolate our l here. If we were to do that, we just have to divide both sides by six Look, which becomes thirty six. So another L squared is equal to thirty six. So from here we can try to get help by square routing both sides because this square in the square, it should cancel out. We should get that l. A is equal to six. So then I must think about the volume of a Q. So we know that the volume is just going to length times, width, times, height because we know length, width and height are all the same because it&#x27;s a cute you could just you tell cute. So if we plug in that l that we found from our surface area into this equation, we should get six cute, and that should just be two sixteen. So we know actually that the volume and the surface area actually be the same for this one.

Melissa Stefan · Answer

here we have a cube that is fully inscribed in a sphere. We know that the volume of the cube is 216 cubic inches. We need to find the volume of the sphere. In order to find the volume of the sphere, we need to know the radius of the sphere. We&#x27;re gonna have to work backwards from are given value of the volume for the Cube in order to find what we need to find the volume of the sphere. What we know is that the diagonal of the Cube is going to equal the diameter ever sphere. So diagonal have. The cube is equal to the diameter of this fear. Of course, if we know the diameter of the sphere, we confined its radius. And if we know its radius, we confined its volume. So first, let&#x27;s find out what the side lengths or the edge length of our cube is. We know the volume is equal to 216 cubic inches. We also know that the volume is equal to the cube of its edge length. So if we have 216 equals s cubed, take the cubed root and we know that each edge is six. I&#x27;m going to redraw the cube so I can get a better idea of what I&#x27;m looking for. With the radius, height is six length of six. With the six we need to know what the diagonal is and to find the diagonal, we can actually create a right triangle here we haven&#x27;t. I saw Seles, right triangle, which gives us this length right here as six square root of two and redraw this right triangle six. This is our six square root to And then, since it&#x27;s a right triangle, we can use a Pythagorean theory room to find the high pot news, which is six square roots of three. So the Diack diagonal of our cube here is six square root three six square root three is equal to the diameter of the sphere. Divide this by two. Three square root three gives us the radius. Now we can take this value and substitute into the volume of a sphere formula, which is 4/3 pi r cubed. To find the volume of this fear, 4/3 pi times three square root three. Cute. Let&#x27;s use a calculator to approximate that to the nearest 10th and we&#x27;ll have let&#x27;s see 4/3 pi times three square root three cute and our volume is approximately 587.7 cubic inches.

Ali Soave · Answer

So if we know that the sphere of the Cube has a volume of 64 then that means it&#x27;s on. We know that a cube has the length, width and depth that&#x27;s all the same. We can take the cube root of 64 that equals four. So all of these links must equal for so because the sphere is inscribed inside of this cube, then that means it&#x27;s diameter must be for a swell, which means half of it would be too. So the surface area of this fear would, before high, too cute or two squared, which would be equal to 16 pi, or about 50 0.3 inches squared.

Michelle Nguyen · Answer

here We have some here. Like Cube. So defined a surface area of a cube. That formula is six a squared. So where to set him equal to each other. So 8 64 equals six a squared Gonna divide both sides by six. So that gives us 1 44 equals a squared would take the square root of both sides. So a is equal to 12. So the edge of the cube is 12.

Erin Kirchmeier · Answer

and this problem were asked to find the volume and surface area of a cube, but with the given dimension. So we know that the side length of the Cuba six inches and since it&#x27;s a cube, we know that all the edges have the same light. So formula for volume of a cube is going to be signed length to the third power. So I&#x27;m gonna take the six, and I&#x27;m going to raise it to the third Power or Cubit. Remember that six times six times six, which gives us a volume off 216 inches. Cute. That&#x27;s a volume. That&#x27;s how much we can fit inside of our box. Next, we&#x27;re gonna talk about surface area, the service area in the box, we calculate by doing six times the sign length squared show ready to six, and then we&#x27;re going to do six squared. So six squared is 36. So we&#x27;re doing six times 36 which gives us a surface area of also 216. But this time, because we&#x27;re calculating area, our units are gonna be inches squared

John Mcalister · Answer

So we&#x27;re interested in the area of a cube. Ah, and remember, a cube is a ah quadrilateral prison. Where all of the cycling through the same in this time, This case, it gives us the fact that all of our side lengths our eight. Right. So, um, we can do this classically, like just doing base times. Height base is gonna be just one of these squares, right? So that the area of our base is gonna be eight times eight, which equals 64. And then our height, of course, is also so volume is gonna equal 64 times eight, which equals 512. Um, also, we could just recognize that because this is a cube, Uh, we know the expression for a cube quickly is just the volume equals the side length cubed. And in this case, our side length is eight. So just eight cube, which equals I have 12 were, you know, we recognize that we&#x27;re doing the same thing, right? This is eight squared times. Another aid is eight cubed. Um, this is just kind of ah ah, A shorter way to keep track of what you&#x27;re doing in your head

Problem

If $\frac{3}{4} y=6-\frac{1}{3} c,$ then what is …

Problem 2 Hard Difficulty

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